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Percolation in a network with long-range connections: Implications for cytoskeletal structure and function

Author

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  • Silveira, Paulo S.P.
  • Alencar, Adriano M.
  • Majumdar, Arnab
  • Lemos, Miriam
  • Fredberg, Jeffrey J.
  • Suki, Béla

Abstract

Cell shape, signaling, and integrity depend on cytoskeletal organization. In this study we describe the cytoskeleton as a simple network of filamentary proteins (links) anchored by complex protein structures (nodes). The structure of this network is regulated by a distance-dependent probability of link formation as P=p/ds, where p regulates the network density and s controls how fast the probability for link formation decays with node distance (d). It was previously shown that the regulation of the link lengths is crucial for the mechanical behavior of the cells. Here we examined the ability of the two-dimensional network to percolate (i.e. to have end-to-end connectivity), and found that the percolation threshold depends strongly on s. The system undergoes a transition around s=2. The percolation threshold of networks with s<2 decreases with increasing system size L, while the percolation threshold for networks with s>2 converges to a finite value. We speculate that s<2 may represent a condition in which cells can accommodate deformation while still preserving their mechanical integrity. Additionally, we measured the length distribution of F-actin filaments from publicly available images of a variety of cell types. In agreement with model predictions, cells originating from more deformable tissues show longer F-actin cytoskeletal filaments.

Suggested Citation

  • Silveira, Paulo S.P. & Alencar, Adriano M. & Majumdar, Arnab & Lemos, Miriam & Fredberg, Jeffrey J. & Suki, Béla, 2009. "Percolation in a network with long-range connections: Implications for cytoskeletal structure and function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1521-1526.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:8:p:1521-1526
    DOI: 10.1016/j.physa.2008.12.024
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    References listed on IDEAS

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    1. Furuta, Tadaomi & Ebina, Kuniyoshi, 2002. "A lattice model for cytoskeletons’ dynamics: analysis of growth and shrinkage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 162-169.
    2. Safran, S.A. & Gov, N. & Nicolas, A. & Schwarz, U.S. & Tlusty, T., 2005. "Physics of cell elasticity, shape and adhesion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(1), pages 171-201.
    3. Moukarzel, Cristian F., 2006. "Percolation in networks with long-range connections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 372(2), pages 340-345.
    4. Rego, Henio H.A & Lucena, Liacir S & da Silva, Luciano R & Tsallis, Constantino, 1999. "Crossover from extensive to nonextensive behavior driven by long-range d=1 bond percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 42-48.
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    Cited by:

    1. M. Kroon, 2011. "Optimal length of smooth muscle assessed by a microstructurally and statistically based constitutive model," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 14(01), pages 43-52.

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